Duality Theory in Fuzzy Linear Programming Problems with Fuzzy Coefficients

The concept of fuzzy scalar (inner) product that will be used in the fuzzy objective and inequality constraints of the fuzzy primal and dual linear programming problems with fuzzy coefficients is proposed in this paper. We also introduce a solution concept that is essentially similar to the notion of Pareto optimal solution in the multiobjective programming problems by imposing a partial ordering on the set of all fuzzy numbers. We then prove the weak and strong duality theorems for fuzzy linear programming problems with fuzzy coefficients.     

Organic synthesis based on cathodic deprotonation of acids

The results of studies on electrosynthesis involving carb- and heteroanions generated by cathodic deprotonation of acids (CDA), carried out in the laboratory headed by the author, are surveyed. These studies resulted in the elaboration of efficient electrochemical versions of the known Michaelis-Becker, Wittig-Horner, and Perkin reactions; electrochemical analogs of homolytic aromatic substitution, alkylation, heterocyclization,etc. were developed. Based on CDA, convenient and promising methods for preparing variousN-, O-, P-, S-, andC-alkylated and arylated substances have been developed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1411–1422, August, 1995.The author is grateful to Professor V. A. Dorokhov, Professor V. P. Litvinov, and researchers from the laboratories of N. D. Zelinsky Institute of Organic Chemistry headed by them, who participated in joint studies.The work was carried out with financial support from the International Science Foundation (Grant No. MHYOO).     

LOCAL SPECTRA OF UNILATERAL OPERATOR WEIGHTED SHIFTS

In this note, the local spectral properties of unilateral operator weighted shifts arestudied.     

Specific heat and related thermophysical properties of liquid Fe-Cu-Mo alloy

The specific heat and related thermophysical properties of liquid Fe77.5Cu13Mo9.5 monotectic alloy were investigated by an electromagnetic levitation drop calorimeter over a wide temperature range from 1482 to 1818 K. A maximum undercooling of 221 K (0.13 Tm) was achieved and the specific heat was determined as 44.71 J·mol-1·K-1. The excess specific heat, enthalpy change, entropy change and Gibbs free energy difference of this alloy were calculated on the basis of experimental results. It was found that the calculated results by traditional estimating methods can only describe the solidification process under low undercooling conditions. Only the experimental results can reflect the reality under high undercooling conditions. Meanwhile, the thermal diffusivity, thermal conductivity, and sound speed were derived from the present experimental results. Furthermore, the solidified microstructural morphology was examined, which consists of (Fe) and (Cu) phases. The calculated interface energy was applied to exploring the correlation between competitive nucleation and solidification microstructure within monotectic alloy.     

关于非齐次m阶马氏信源的渐近均分割性

本文研究非齐次m阶马氏信源的渐近均分割性，首先我们得到关于此种信源m 1元函数的一类强极限定理，作为推论，得到关于任意非齐次m阶马氏信源状态和熵密度的几个极限定理，最后得到一类非齐次m阶马氏信源的渐近均分割性。     

四溴双酚A锑铝双金属化合物的合成及其阻燃性能

以四溴双酚Ａ（ＴＢＡ）合成了在水和空气中稳定的四溴双酚Ａ合锑铝双金属化合物（ＴＢＡＳＡ）．通过ＩＲ、１ＨＮＭＲ和元素分析予以表征，并研究了其对聚乙烯（ＰＥ）和聚环氧乙烷（ＰＥＯ）的阻燃性能．结果表明，这种分子中含有溴、锑和铝的化合物，对聚乙烯和聚环氧乙烷等高聚物材料有高的阻燃性能与消烟效果．     

Banach-Saks property in Marcinkiewicz spaces

We catalogue all Marcinkiewicz function and sequence spaces with the Banach-Saks property and present necessary and sufficient conditions for a wide subclass of spaces to possess the p-Banach-Saks property, 1<p<∞. We apply our results to several open problems.     

On the properties of solutions to the Goursat-Darboux problem with boundary and distributed controls

We consider a control system described by the Goursat-Darboux equation. The system is controlled by distributed and boundary controls. The controls are subject to the constraints given as multivalued mappings with closed, possibly nonconvex, values depending on the phase variable. Alongside the initial constraints, we consider the convexified constraints and the constraints whose values are the extreme points of the convexified constraints. We study the questions of existence of solutions and establish connections between the solutions under various constraints.     

Study of intermediates formed in the oxidation of thiols

The oxidation of aminoethanethiol (1) was investigated in acid solutions on a glass carbon anode. It was shown that at relatively low anode potentials thiyl radicals RS^· are released into the solution, but this does not lead to binding of the oxygen in the solution. Raising the anode potential leads to binding of oxygen, which is probably due to the formation of the intermediate RS⁺. The oxidation of 1 was studied in Ce(SO₄)₂+H₂SO₄ solution. It was shown that under certain conditions the intermediate is RS⁺, which subsequently converts to a product that could not be identified as any previously described product of the oxidation of thiols. Proposals are made regarding its structure and conversion pathways.B. P. Konstantinov Institute of Nuclear Physics, Russian Academy of Sciences, 188350 Leningrad. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 2, pp. 278–288, February, 1992.     

The fixed point property for multivalued nonexpansive mappings

We show some properties concerning geometrical constants of Banach spaces which imply the existence of fixed points for multivalued nonexpansive mappings and we study the relationship between these properties.